USIMD: Optimize the performace of np.einsum for all platforms

[Qiyu8]

seven sub module of np.einsum is optimized using neon intrinsics. The optimization resulted in a performance improvement of 10~42%.

System info:

• HardWare: KunPeng
• Processor: ARMv8 2.6GMHZ 8 processors
• OS: Linux ecs-9d50 4.19.36-vhulk1905.1.0.h276.eulerosv2r8.aarch64

The optimization effect:

einsum sub module triggered	master	einsum-neon	ratio
sum_of_products_stride0_contig_outstride0_two	110±0.5μs	100±0.5μs	0.90
sum_of_products_contig_stride0_outstride0_two	110±0.5μs	101±0.5μs	0.90
sum_of_products_contig_stride0_outcontig_two	23.7±1ms	20.2±0.3ms	0.85
sum_of_products_contig_two	152±0.8μs	140±2μs	0.91
sum_of_products_stride0_contig_outcontig_two	946±10μs	841±20μs	0.89
contig_contig_outstride0_two	522±5μs	353±7μs	0.68
sum_of_products_contig_outstride0_one	871±10μs	502±4μs	0.58

[mattip]

We discussed this briefly in the sprint. Correct me if I am wrong: this is a reimplementation of the SSE2 intrinsics in NEON. I wonder if we could already use the universal intrinsics to make this generic?

[Qiyu8]

I'd be happy to change it to universal intrinsics，Is there any guidance document or example that I should read first? @mattip @seiko2plus

[seiko2plus]

I'd be happy to change it to universal intrinsics，Is there any guidance document or example that I should read first?

not yet, but sure I can guide you

[seiko2plus]

replace these intrinsics with:
vld1q_f64 -> npyv_load_f64
vmulq_f64 -> npyv_mul_f64
vaddq_f64 -> npyv_add_f64
vst1q_f64 -> npyv_store_f64

for more intrinsics, you have to search or dive in the NPYV

[seiko2plus]

BTW why you didn't use FMA3 here, well currently there's no mul-add intrinsic in NPYV but I guess It will not be that hard to impmlent it.

[Qiyu8]

I will make another PR for mul-add intrinsic in NPYV.

[Qiyu8]

@seiko2plus Thanks for your advice, Reconstruct einsum using Universal SIMD after reading simd-optimizations.rst, here is the routine:
1- Configuration: add a dispatch file to corresponding module that needs to optimized, remember to add to setup.py for compiler purpose.
2- Rewrite: rewrite the original platform's related intrinsics by using NPY_SIMD and npyv simd api
3- Test Case: write a SIMD dispatch test case to the caller module. in this case it's multiarraymodule.c, then add to test_cpu_dispatcher in order to trigger this test case.

I just make @name@_sum_of_products_contig_two function an example, correct me if i were wrong, then I will rewrite other functions by following this pattern.

PS: USIMD is really powerful, saved so much coding time. 😃

[mattip]

nice to see use of the universal intrinsics.

[mattip]

@seiko2plus shouldn't we be generating files in build/* rather than in the source directories, or is this similar to cython-generated files?

[seiko2plus]

yes, should be generated into build/src.*, but maybe @Qiyu8 use --inplace.

[Qiyu8]

yes, I used -i option during build.

[seiko2plus]

I guess you used inplace option -i because you received error like that

: fatal error: einsum.dispatch.h: No such file or directory

well it's my bad, CcompilerOpt should include build/src.*/numpy/core/src/multiarray to the search dir, even if it wasn't added by 'core/setup.py'.

This issue should be fixed by #16858.

[mattip]

#16858 is merged.

[seiko2plus]

thank you @mattip.

[Qiyu8]

I think we should keep this ignore part, I build the source with -i option, and the *.dispatch.*.c will generated.

[mattip]

By default people should not be using -i since it messes up the source directory, as you discovered. Why don't you want to use the build directory? Is there another problem that using -i fixes?

[Qiyu8]

build directory is good , no problem if I don't use -i option. will remove from ignore list.

[mattip]

It would be good at some point to rename these with meaningful names. Is there a reason to have the different size variants? Perhaps a very small variant would be good as well.

[Qiyu8]

@mattip I found that meaningless naming is pretty common in every bench module, should we open a separate rename PR? I want to focus on the universal intrinsics transform process in this PR.

[mattip]

ok. What about adding a very small variant as well?

[Qiyu8]

I doubt that small variant is not enough to evaluate the degree of optimization, I will test with small size and provide a report anyway.

[seiko2plus]

@Qiyu8, you should dispatch the tabs that hold the functions pointers within PyArray_EinsteinSum() and also there's no need to defining tests. could you please allow me to help you? I'm just gonna initialize the dispatching process for you and then you will handle the universal intrinsics part.